Incorporating machine-learning models into log-optimal e-variable design

Develop methods for incorporating machine-learning models into the design of log-optimal e-variables for model-X conditional-independence testing.

Background

The paper studies sequential conditional-independence testing under the model-X assumption, where the conditional distribution of an input given the remaining covariates is specified or estimated. Log-optimal, or growth-rate-optimal, e-variables are theoretically attractive, but their construction typically involves an unknown conditional density that is difficult to estimate with predictive machine-learning models.

The authors identify the unresolved issue of how to use machine-learning predictors—rather than explicit conditional-density models—to construct effective log-optimal e-variables. This motivates their exponential-loss-based construction and comparison with antisymmetric e-variables, but the general problem remains unresolved.